Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesEasy2 minPYQ_2021

MathematicsEasysingle choice

The area of the region bounded by $y - x = 2$ and $x^{2} = y$ is equal to :-

Answer:

Solution:

$y - x = 2, x^{2} = y$

Now, $x^{2} = 2 + x$

$\Rightarrow x^{2} - x - 2 = 0$

$\Rightarrow (x + 1) (x - 2) = 0 \Rightarrow x = - 1, 2$

Required area $= \int_{- 1}^{2} (2 + x - x^{2}) d x$

$= {|2 x + \frac{x^{2}}{2} - \frac{x^{3}}{3}|}_{- 1}^{2}$

$= (4 + 2 - \frac{8}{3}) - (- 2 + \frac{1}{2} + \frac{1}{3})$

$= 6 - 3 + 2 - \frac{1}{2} = \frac{9}{2}$ square units

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2021

Loading discussions...